We use the recently developed brozone theory of plastic deformation [1] to investigate the transmission of high stresses to the neighborhood of a defect in a solid material. Here, we correct and extend previous findings on the expansion of a circular hole in a large plate [2]. By taking advantage of the simple geometry of the problem, we are able to observe analytically features such as linear vis co elastic flow at small stresses, strain hardening at larger stresses, and a dynamic transition to vis co plas tic ity at the yield stress. Our analysis predicts the formation of a well-defined plastic zone around the hole for hard materials, and a more diffuse plastic zone for soft materials. The deviatoric stress always exceeds the yield stress on the boundary of the hole, but its value also depends on the softness of the material. We study the shape stability of the hole and speculate that our results may be related to the dynamics of fracture. [1] M.L. Falk and J.S. Langer, Phys. Rev. E 57, 7192 (1998). [2] J.S. Langer and A.E. Lobkovsky, Phys. Rev. E 60, 6978 (1999)